Cancer cells differ in size from those of their host tissue and are known to change in size during the processes of cell death. A noninvasive method for monitoring cell size would be highly advantageous as a potential biomarker of malignancy and early therapeutic response. This need is particularly acute in brain tumours where biopsy is a highly invasive procedure. Here, diffusion MRI data were acquired in a GL261 glioma mouse model before and during treatment with Temozolomide. The biophysical model VERDICT (Vascular Extracellular and Restricted Diffusion for Cytometry in Tumours) was applied to the MRI data to quantify multi-compartmental parameters connected to the underlying tissue microstructure, which could potentially be useful clinical biomarkers. These parameters were compared to ADC and kurtosis diffusion models, and, measures from histology and optical projection tomography. MRI data was also acquired in patients to assess the feasibility of applying VERDICT in a range of different glioma subtypes. In the GL261 gliomas, cellular changes were detected according to the VERDICT model in advance of gross tumour volume changes as well as ADC and kurtosis models. VERDICT parameters in glioblastoma patients were most consistent with the GL261 mouse model, whilst displaying additional regions of localised tissue heterogeneity. The present VERDICT model was less appropriate for modelling more diffuse astrocytomas and oligodendrogliomas, but could be tuned to improve the representation of these tumour types. Biophysical modelling of the diffusion MRI signal permits monitoring of brain tumours without invasive intervention. VERDICT responds to microstructural changes induced by chemotherapy, is feasible within clinical scan times and could provide useful biomarkers of treatment response.